Ps formation, cooling and emission into vacuum

from porous materials

Positron in Astrophysics 19 march 2012 – Murren

R.S. Brusa Department of Physics –University of Trento

main motivation

Many experiments with positrons require high yield of cooled Ps

In particular we need cooled Ps for AEgIS Hbar experiment and Ps spectroscopy at

CERN

eHPsp**)(

Outline

•Positronium emission from surface

•Ps collisional cooling and

Ps thermalization in porous material

Ps at surfaces

Backscattered Ps

SOLID

Hot Ps, Ps* from epithermal e+

Hot Ps, Thermal Ps from thermal e+

After Steiger and Conti 1992

Calculated density of e+ returning at the Al surface, solid line 1keV e+

dashed line 50 eV e+

1 Thermal e+ 2 Epithermal e+ 3 Backscattered e+

Time of flight measurement with e+ beams

The perpendicular velocity is measured v2

22

2

1

t

zmvmE ePs

Backscattered Ps and Ps by epithermal e+

After Howell 1986

Backscattered Ps has a energy dependence approximately as E-1 where E is the e+ incident energy

TOF spectra of Ps emitted from Cu Hatched area , spectrum of Ps from epithermal e+

Ps formation and emission by thermal e+

Direct Ps formation Ps formation by trapped positron at the surface

Direct Ps formation and emission by thermal e+

Possible when the positronium formation potential is negative

Pink: No surface Ps emission εPs >0 -White : Ps emission εPs < 0 Blue: competition between Ps emission and e+ emission

continuous energy spectrum up to the Fermi energy level in metals.

Thermal Ps emission- surface trapping

After Shultz and Lynn 1988

e+ can fall in a trapped state localized In few Amstrong from the surface e+ is strongly correlated with the electron cloud. In figure two extreme: image potential - bare positron Van der Waals - virtual positronium-like

Al Ps emission require an energy Ea , and thermal activation is possible

Ps emission from dielectrics •Ps formation by thermal positron reaching the surface is, in most cases, energetically forbidden. The 6.8 eV energy gain of Ps formation is not enough to extract an electron •Formation of Ps can occur in the bulk. Ps reaching the surface can be emitted If its work function is negative •Ps can form and be hosted by open volumes in dielectrics. If there is a open volume defect network , hopping diffusion may lead to Ps emission into vacuum

In quartz and amorphous SiO2 two different Ps components were observed : One around 1 eV attributed to Ps formed in the bulk One around 3 eV by electron capture of an electron at The surface

Nagashima et al. 1998

1nm Ps

e+

Ps

Ps

Ps

e+

e+

Ps cooling using porous SiO2 based materials

1nm Ps

e+

Ps

Ps

Ps

e+

e+

Ps is formed with eV energy but lose energy by collision with the walls of the connected porosities. Ps energy is normally insufficient for electronic excitation, Ps lose energy by exciting atomic motion A fraction of oPs can reach the surface and can be emitted cooled into the vacuum.

Ps cooling by collisions

Competitive effect : Ps pick-off

oPs 2γ

L

vPsoffpick

Pick off : when the e+ in Ps has an

overlap with an e- of the walls in

an interaction region R

It is expected : to depend from cooling time: ie. permanence

in the excited states

Ps cooling and quantum confinement

Ps cooling process can be described in two regimes:

HIGH ENERGY LIMIT: de Broglie wavelength is small respect to the dimension d of the cavity

meVd

nm

dm

hE

o

206

4 2

2

E

meVnm

206

Ps can be considered a free object of size:

Ps collisions can be treated as a classical elastic scattering ( Sauder , J. Res. Natl. Bur. Stand. § A ,72, (1968) 91)

Ps cooling and quantum confinement

LOW ENERY REGIME

The interaction between the Ps atom and the walls can be described in terms of the contact between a confined Ps atom with the solid as a whole. An estimation of the minimum T permitted for a Ps atom confined in nano-pores and nano-channels, when the temperature is lowered, can be made by modeling the Ps cooling by creation and destruction of phonons at the surface of the pores. (Mariazzi ,Salemi, Brusa, PRB 2008).

meVd

nm

dm

hE

o

206

4 2

2

the maximum variation of the momentum magnitude of Ps due to the exchange of a single phonon at the first order

1-8

maxmax m10*7.1

2

mvkkk sI

Ps cooling and quantum confinement

0 5 10 15 20 25 30

10

100

b)

Ps tem

pera

ture

[K

]

Side a [nm]

0,0

2,0x103

4,0x103

6,0x103

8,0x103

a)

222

2

a

n

mE m

222

33

2

a

n

mkE

kT m

BB

Minimum energy and minimum temperature of a Ps atom confined in a cubic box of size a

mn is the lower accessible level

Dashed line :ground level in a cubic box

Continuous line : ground state = minimum level in Nano-channels (infinite well)

Mariazzi S, Salemi A and Brusa R S 2008 Phys. Rev. B 78 085428

Ps

Positronium converter

Positron beam

Ps

Ps

Vacuum

Ps

Ps

222 / amEg

gB EkT )3/2(

the minimum temperature is:

Mariazzi S, Salemi A and Brusa R S 2008 Phys. Rev. B 78 085428

#0 (4-7 nm) mini T is 180-60 K #1 (8-12 nm) min T is 45-20 K

160 K

Nano-size and Ps thermalization

Si p-type 0.15-0.21 Ohm/cm current from 4-18 mA/cm2 , 15’

produced by electrochemical etching, as for porous silicon but adapting times and current for obtaining nano- structures

10 nm #0 #1 #2 #3 #4

100 nm

#5

Possibility of tuning: #0 = 4-7 nm #1=8-12 nm #2= 8-14 nm # 3= 10-16 nm #4= 14-20 nm #5= 80-120 nm

Mariazzi S, Brusa R S et al Phys. Rev. B 81, 235418 (2010)

Tuning the size of nanochannels

Trento slow positron beam (50 eV-30 keV)

470 480 490 500 510 52010

0

101

102

103

104

coun

ts

energy ( keV )

2γ rays peak area

o-Ps 3γ rays valley area

Annealed 1h 300°C

Annealed 2h 100°C #0

10 nm

a) b)

0.1 1 10

0.0

0.1

0.2

0.3

0.4

0.5

Mean positron implantation depth [nm]

not oxidized

0.5h 100°C

2h 100°C (#0)

4h 100°C

1h 300°C

1h 400°C

F3 (

o-P

s fr

actio

n)

Positron implantation energy [keV]

10 1000

Optimum oxidation for the Ps yield

0.1 1 10

0.1

0.2

0.3

0.4

0.5

Mean positron implantation depth [nm]

F3 (

o-P

s fr

actio

n)

Positron implantation energy [keV]

#3

#4

#5

0.1

0.2

0.3

0.4

0.5

#0

#1

#2

10 1000

ECEBEAEF )(3

12

1

121

E

E

eFFFEA

6.1

0

1

1

E

EEB

2

2

21

1

C

E

E

CCKEC

o-Ps formation

o-Ps out diffusion probability

o-Ps annihilation via 3γ into pores

Ps yield and channel size

#0 = 4-7 nm #1=8-12 nm #2= 8-14 nm # 3= 10-16 nm #4= 14-20 nm #5= 80-120 nm

200

400

600

800

1000

1200

1400

1600

#0 #1 #2 #3 #4 #5

o-P

s d

iffu

sio

n length

[nm

]

Sample

The o-Ps fraction out-diffusing at 10 keV positron implantation energy is still 10 % in #0 = 4-7 nm 17 % in #1 = 8-12 nm 23-25 % in #2, #3, #4 and #5 15 - 100nm

Up to 42 % of implanted positrons at 1 keV emitted as o-Ps

LPs

0.1 1 10

0.1

0.2

0.3

0.4

0.5

Mean positron implantation depth [nm]

F3 (

o-P

s fr

actio

n)

Positron implantation energy [keV]

#3

#4

#5

0.1

0.2

0.3

0.4

0.5

#0

#1

#2

10 1000

0 2 4 6 8 10 12 14 16 180

10

20

30

40

50

60

70

Inte

nsity [

%]

Positron implantation energy [keV]

I1

I2

I3

0.2

0.4

0.6

20

30

40

50

60

1

2

3

Life

tim

e [n

s]

2 channeltrons

target position

5 NaI scintillators

Trento TOF Apparatus BEAM

Prompt peak 16 ns

zo

The TOF apparatus of Trento is now at the intense positron source NEPOMUC at the FRMII reactor in Munich and will be set up at the reactor hall in June-July. NEPOMUC gives 10 9 e+ /s

zo

o-Ps Time of Flight measurements

where

tf

tp

z0

If tp ˂˂ tf tm tf

Mariazzi S, Brusa R S et al., Phys. Rev. Lett. 104 243401 (2010)

0 50 100 150 200 250

0.068 eV

co

un

ts [

arb

itra

ry u

nits]

o-Ps time of flight [ns]

7 keV, T = 150 K

2

0.076 eV

7 keV, T = 200 K

0 100 200 300 400

FWHM = 23 ns

counts

[arb

. units

]

Time of flight [ns]

Prompt

0.096 eV

7 keV, T = 300 K3

4

8

0.140 eV 4 keV, T = 300 K

After smoothing, subtraction of the background, and correction by multiplying by

142

exp1 tt

Ps cooling - 5-8 nm channels

0.0 0.1 0.2 0.3

T=1515±15K

T=305±10K

T=1425±25K

T=195±10K

T=1260±15K

T=145±10K

7 KeV, T = 300 K

7 KeV, T = 200 K

7 KeV, T = 150 K

log(

dN

/dE

) [a

rbitr

ary

uni

ts]

o-Ps kinetic energy [eV]

dEENdttN )()(

3)()( ttNEN

0 50 100 150 200 250

0.068 eV

co

un

ts [a

rbitra

ry u

nits]

o-Ps time of flight [ns]

7 keV, T = 150 K

2

0.076 eV

7 keV, T = 200 K

0 100 200 300 400

FWHM = 23 ns

counts

[arb

. units

]

Time of flight [ns]

Prompt

0.096 eV

7 keV, T = 300 K3

4

8

0.140 eV 4 keV, T = 300 K

The two lines in log-lin graph are proportional to at two different T.

Ps energy

Mariazzi , Bettotti, Brusa, 2010 Phys. Rev. Lett. 104 243401

With A and B , normalization factors

Analysis of the Ps energy spectra

Cool distribution

Warm distribution

Ps

Positronium converter

Ps

Ps

Vacuum

Ps

Ps

Permanence time of Ps in nano-channels before escaping into vacuum

<tm> = <tp> + <tf>

tf

tp

z0

Measurements at three different distances z0 allow to evaluate <tp>

Measurements were done at 7 keV e+ energy

0.00 0.05 0.10 0.15 0.20

z0 = 3 cm, 7 keV

z0 = 2 cm, 7 keV

1130±115 K

339±30 K

910±90 K

331±10 K

1688±150 K

290±17 K

log

(dN

/dE

) [

arb

. u

nit

s.]

Ps kinetic energy [eV]

z0 = 1 cm, 7 keV

Ps energy spectra Ps energy spectra

<tm> of the cold and

warm distribution

<tm> = <tp> + z0/v

tf tp

z0

<tcp> =18±6 ns

<tcw> < 7 ns

Cooling time of Ps

conclusion with a question

Study of Ps formation and annihilation in complex materials and porous complex materials at low temperature are lacking Could be more data useful for understanding signal of Ps annihilation in ISM ?

Thanks for listening and Thanks to the organizers

for the invitation and the wonderful workshop

From Schilthorn